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Math on the Spot Video Tutor Online Assessment

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Resources

e

Texas Essential Knowledge and Skills

Number and Operations—5.3.C Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm Also 5.3.A

MATHEMATICAL PROCESSES5.1.B Use a problem-solving model

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 2.6 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

2.6 Divide by 2-Digit Divisors How can you divide by 2-digit divisors?Essential Question?

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about division of whole numbers.

When do we use division to solve a problem? (to find how many equal-sized groups are in a set of objects [partitive division], or how to find the number of groups of a given size within a set of objects [quotative division]) What is one way to estimate a quotient? (Possible answer: Divide compatible numbers.)

Using the Digital LessonTalk about using division to figure out calendar information. For example, if a student knows how many hours were spent doing homework in a month and needs to find about how many hours were spent doing homework in a day.

Learning Task• What information is given in this problem? (the number of miles a car traveled

and the number of miles the car travels on one gallon of gas—its MPG)

• What do we have to find? (about how many gallons of gas were used on the trip)

• What strategy can you use to solve the problem? (divide 1,407 by 32) Why? (Possible answer: I am looking for the number of equal groups of 32 in 1,407.)

Literacy and Mathematics• Write the acronym MPG on the board and explain what it means. Then, tell students

that different types of cars have different MPG ratings. Ask students how the MPG ratings of small cars and large cars may vary. Then, have students give reasons why a greater MPG rating is better than a lesser one.

• Tell students that a typical fuel tank in a compact car holds about 15 gallons of gas. Ask them to calculate about how many miles a car might go if its MPG rating was 45.

How can you divide by 2-digit divisors?

Lesson 2.6 85A

Essential Question?

Unlock the ProblemUnlock the Problem

Mathematical ProcessesMath Talk

Number and Operations—5.3.C Also 5.3.A

MATHEMATICAL PROCESSES5.1.B

2.6Name

How can you divide by 2-digit divisors?

Divide by 2-Digit Divisors

Mr. Yates owns a smoothie shop. To mix a batch of his famous smoothies,

he uses 18 ounces of orange juice. Each day he uses 560 ounces of orange

juice. How many batches of smoothies can Mr. Yates make in a day?

• Underline the sentence that tells you what you are trying to find.

• Circle the numbers you need to use.

Divide. 560 ÷ 18 Estimate. ___

STEP 1 Use the estimate to place the first digit in the quotient.

18 ) ‾ 560 The first digit of the quotient will be in the __ place.

STEP 2 Divide the tens.

3 18 ) ‾ 560

−54

2

56 tens ÷ 18Divide. ____

Multiply. ____

Subtract. ____

Check. 2 tens cannot be shared among 18 groups without regrouping.

STEP 3 Divide the ones.

31 18 ) ‾ 560

−54

20 −18

_

2

r2

Divide. ____

Multiply. ____

Subtract. ____

Check. ____

____

Since _ is close to the estimate of 30, the answer is reasonable.

So, Mr. Yates can make _ batches of smoothies each day.

Explain what the remainder 2 represents.

600 ÷ 20 = 30

tens

31

31

18 × 3 tens = 54 tens

56 tens − 54 tens

20 ones ÷ 18

18 × 1 one = 18 ones

The remainder represents the 2 ounces of orange juice left over after the 31 batches are made.

20 ones − 18 ones

2 ones cannot be shared

among 18 groups.

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Module 2 85

English Language Learners Language SupportELL

9 8 2 92 1 ,

ELPS 2.I.3, 3.C.4, 3.D.2Leveled Activities ELPS

Beginning: Activity 19 1.A.1, 3.E, 4.F.7

Intermediate: Activity 22 1.A.1, 3.G.1, 4.C.1

Advanced: Activity 46 1.F, 2.I.4, 4.G.2

Advanced High: Activity 35 1.B.1, 1.F, 3.C.4, 3.G.2

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: Describe• Students describe the process of solving a division

problem using the traditional algorithm.• Show students a division problem. Students take

turns describing how to solve the problem.• Have students focus on how to determine each digit in the quotient.

Lead them by asking, “How did you find this digit?” or “How do you know if this digit is too low or too high?”

Auditory Small Group

Unlock the ProblemDo you know what a smoothie is? Read the problem to learn the answer.

After students underline and circle the relevant information, ask:

• Why is division used to solve this problem? Possible answer: Division involves the number of groups, the number in each group, and the whole. In this problem, we know that 560 ounces is the whole and that there are 18 ounces in each group. So, we divide 560 by 18 to find the number of groups.

Discuss the solution.

• In Step 2, we divide the tens. Why can’t we divide the hundreds? Possible answer: 5 hundreds cannot be divided into 18 equal groups without regrouping.

• How many tens are we dividing in Step 2? Explain. We are dividing 56 tens; 5 hundreds 6 tens were regrouped as 50 tens 6 tens, or 56 tens altogether.

After discussing the solution, ask:

• Why wasn’t the remainder included as part of our answer? Possible answer: It is not reasonable for Mr. Yates to make a partial batch of smoothies.

Math Talk Use Math Talk to focus on students’ understanding of what remainders represent in various division problems.

Mathematical Processes

85 Module 2

Example

Share and ShowShare and Show

Every Wednesday, Mr. Yates orders fruit. He has set aside $1,250 to

purchase Valencia oranges. Each box of Valencia oranges costs $41.

How many boxes of Valencia oranges can Mr. Yates purchase?

You can use multiplication to check your answer.

Divide. 1,250 ÷ 41

DIVIDE CHECK YOUR WORK

Estimate. ___

41 1,2503030 r20

) ‾ × 4130–

+ +1,2001,250 –

So, Mr. Yates can buy _ boxes of Valencia oranges.

1. 28 ) ‾ 620 2. 64 ) ‾ 842 3. 53 ) ‾ 2,340

4. 723 ÷ 31 5. 1,359 ÷ 45 6. 7,925 ÷ 72

Divide. Check your answer.

1,200 ÷ 40 = 30

1,2301232020

1,230020

30

22 r4 13 r10 44 r8

23 r10 30 r9 110 r5

86

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Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich VisualIndividual

• Many distance records have been set and then broken for hot-air balloons. Have students use the information below to find which balloon flight had the fastest average speed in miles per hour. (Hint: Speed = distance ÷ time) 2,900 ÷ 33 is 87 r29; 6,700 ÷ 47 is 142 r26; 26,542 ÷ 472 is 56 r110. So, the 1991 hot air balloon flight had the fastest average speed.

ExampleAsk the question shown below as you discuss the divide step of the solution.

• The division step shows the completed solution. Look at the first digit in the quotient. Explain how division, multiplication, and subtraction were used for that digit. Compatible numbers and division were used to identify and place the first digit in the quotient. Multiplication was used to find the amount we subtract. Then subtraction was used to continue the division.

Consider the same question for the second digit in the quotient.

Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 14

Hot-Air Balloon Distance Records

Year Distance Traveled (miles) Time (hours)

1987 2,900 33

1991 6,700 47

1999 26,542 472

Lesson 2.6 86

Problem SolvingProblem Solving

Problem SolvingProblem Solving

20 ounces cranberry juice10 ounces passion fruit juice

18 ounces orange juice12 ounces mango juice

22 ounces grape juice8 ounces apple juice

Royal Purple Smoothie

Orange Tango Smoothie

Crazy Cranberry Smoothie

Name

Use the list at the right to solve 14–16.

14. A smoothie shop receives a delivery of

980 ounces of grape juice. How many Royal

Purple smoothies can be made with the

grape juice?

15. Multi-Step

The shop has 1,260 ounces

of cranberry juice and

650 ounces of passion fruit

juice. If the juices are used

to make Crazy Cranberry

smoothies, which juice will run out first?

How much of the other juice will be left

over?

Practice: Copy and Solve Divide. Check your answer.

7. 775 ÷ 35 8. 820 ÷ 41 9. 805 ÷ 24

10. 1,166 ÷ 53 11. 1,989 ÷ 15 12. 3,927 ÷ 35

13. Why can you use multiplication to check division? Explain.

16. In the refrigerator, there are 680 ounces of orange juice

and 410 ounces of mango juice. How many Orange Tango smoothies can

be made? Explain your reasoning.

44 smoothies

cranberry juice; 20 ounces of passion fruit juice will be left over

34 smoothies; Possible explanation: The orange juice can be used in 37 Orange Tango

smoothies, and the mango juice can be used to make 34 Orange Tango smoothies. You

will run out of mango juice after 34 smoothies.

22 r5 20 33 r13

22 132 r9 112 r7

Possible answer: Since multiplication is the inverse operation of division, the product

should be close to the dividend, even without adding the remainder.

Module 2 • Lesson 6 87

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Name

When you divide by a 2-digit divisor, you can use estimation to help you place the first digit in the quotient. Then you can divide.

Divide. 53 ) - 2,369

Step 1 Use compatible numbers to estimate the quotient. Then use the estimate to place the first digit in the quotient.

The first digit will be in the tens place.

Step 2 Divide the tens.

Step 3 Bring down the 9 ones.Then divide the ones.

So, 2,369 ÷ 53 is .

Divide. Check your answer.

1. 52 ) -

612 2. 63 ) -

917 3. 89 ) -

1,597

4. 43 ) -

641 5. 27 ) -

4,684 6. 64 ) -

8,455

Divide by 2-Digit DivisorsOBJECTIVE Divide by 2-digit divisors.

LESSON 14

Think:

Divide: 236 tens ÷ 53

Multiply: 53 × 4 tens = 212 tens

Subtract: 236 tens - 212 tens

Compare: 24 < 53, so the first digit of the quotient is reasonable.

Think:

Divide: 249 ones ÷ 53

Multiply: 53 × 4 ones = 212 ones

Subtract: 249 ones - 212 ones

Compare: 37 < 53, so the second digit of the quotient is reasonable.

Write the remainder to the right of the whole number part of the quotient.

44 r37

50 ) - 2,000

53 )- 2,369 -212

24

53 ) - 2,369 -212

249-212

37

40

4

44 r37

11 r40

14 r39

14 r35

173 r13

17 r84

132 r7

Check students’ work.

Number and Operations 27 © Houghton Mifflin Harcourt Publishing Company

Name

E14

Enrich 14

Enrich

14 366) ———

START

5

5 r12

27 951)—–––

58 933)———

18 1,981)—————

39 1,600)—————45 548)————

48 3,120)————

66 4,800)————

79 1,264)————

15 1,230)—————

65

12

64

35 r635 r16

111

110 r1

16 r16

16 r5

80 r2

16

17

72 r48

72 r58

12 r8

22 122)————

41 r1

FINISH

40 r38

16

26 r2

A-Mazing Division

Solve each division problem, beginning at START. Draw a line from

the problem to the correct quotient. Continue until you reach FINISH.

If you reach a dead end, go back and try again.

82

Enrich 14RtI Tier 1 Lesson 14

COMMON ERRORSError When dividing, subtraction produces a number that is greater than or equal to the divisor.

Example

Springboard to Learning Point out that the division cannot continue when the difference is greater than or equal to the divisor. Have these students compute the result of increasing the corresponding digit in the quotient by 1.

CE

Problem SolvingBefore students complete the exercises, ask them to describe two different ways to check their answers. One way is to compare the exact answer to the estimate that was used to place the first digit and decide if the exact answer is reasonable. Another way is to multiply the divisor by the quotient, add the remainder to the product, and see if the result is equal to the dividend.

ProblemProblem 16 requires students to analyze the recipes to determine the number of smoothies that can be made with the given ingredients.

63 ) ‾ 1,953 −1 26 69

2

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

1

2

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87 Module 2

Daily Assessment TaskDaily Assessment Task

Mathematical Processes

TEXAS Test Prep 20. James has 1,836 marbles. He decides to divide them equally among

23 boxes. How many marbles will James have left over?

A 19

B 23

C 90

D 79

Fill in the bubble completely to show your answer.

17. A shipment of 572 scented erasers has arrived at the school store.

You want to sell them in sets of 15. How many full sets of erasers

can you make?

A 40 C 39

B 38 D 37

18. Darius counted that he walks 864 steps from his house to the bookstore.

If Darius takes 52 steps each minute, about how long will it take him to

reach the bookstore?

A 31 minutes

B 17 minutes

C 13 minutes

D 20 minutes

19. Multi-Step The school store has 1,262 bouncy balls. The bouncy

balls are packaged in sets. Any single bouncy ball is sold for $1.

If all the bouncy balls sell, which of the following will give the store

the best profit?

A Sets of 25 for $13

B Sets of 16 for $9

C Sets of 12 for $7

D Sets of 10 for $6

88

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Differentiated Centers Kit

THENIF

YES

NO

Daily Assessment Task 1

2

3

• Enrich 14

• Homework and Practice Lesson 2.6

• Soar to Success MathWarm-Up 13.39

LiteratureA Drive Through HistoryStudents read about how the Alverez family uses multiplication and division to plan their vacation

ActivitiesDecide and DivideStudents complete purple Activity Card 15 by estimating quotients and then dividing 3-digit dividends by 2-digit divisors.

ActivitiesDivide and ConquerStudents complete orange Activity Card 15 by making and solving problems with 3-digit dividends and 2-digit divisors.

TEXAS Test Prep CoachIn the Test Prep exercise, if students selected:

B They used the divisor instead of the remainder.

C They used estimation.

D They used the quotient instead of the remainder.

Essential Question? WriteMathWriteMath

How can you divide by 2-digit divisors? Possible answer: First, I use compatible numbers and an estimate to place the first digit. Then, I repeat these steps: divide, multiply, subtract and compare, and then regroup when necessary.

Can students divide by 2-digit numbers?

Lesson 2.6 88

TEXAS Test PrepLesson CheckLesson Check

13. Tamera has a rubber band ball made of

3,241 rubber bands. How many complete

smaller rubber band balls can she make if

each small ball is made of 80 bands?

A 28

B 40

C 53

D 41

14. Sam picks out a book that has 468 pages. He

wants to finish the book in 36 days. If he reads

the same number of pages each day, how

many pages should he read?

A 23

B 17

C 13

D 11

15. A baker has 834 fluid ounces of muffin batter.

Each muffin needs 12 fluid ounces of batter.

How many muffins can the baker make?

A 70

B 69

C 68

D 65

16. Springfield has an aquarium that holds

336 gallons of water. It takes 24 hours to fill

the aquarium. How many gallons of water

fill the aquarium each hour?

A 16 gallons

B 14 gallons

C 15 gallons

D 13 gallons

17. Multi-Step A juice bar has 768 ounces of

passion fruit juice and 810 ounces of berry

juice. Passion fruit juice is sold in 16-ounce

cups. Berry juice is sold in 18-ounce cups.

Which statement is true?

A The juice bar can sell 3 more cups of

berry juice than passion fruit juice.

B The juice bar can sell the same number

of cups of berry juice and passion fruit

juice.

C The juice bar can sell fewer than 90 total

cups of berry juice and passion fruit

juice.

D The juice bar can sell 3 more cups of

passion fruit juice than berry juice.

18. Multi-Step A city has 7,204 recycle bins. The

city gives half of the recycle bins to its citizens.

The rest of the recycle bins are divided into

23 equal groups for city parks. How many

recycle bins are left over?

A 14

B 156

C 138

D 28

Fill in the bubble completely to show your answer.

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90

Problem SolvingProblem Solving

Name

Homeworkand Practice

Divide. Check your answer.

1. 18 ) ‾ 783 2. 22 ) ‾ 4,722 3. 56 ) ‾ 891

4. 19 ) ‾ 3,192 5. 63 ) ‾ 173 6. 43 ) ‾ 8,382

7. 39 ) ‾ 5,109 8. 32 ) ‾ 832 9. 14 ) ‾ 573

Explain.

10. You can check your answer to a division problem by using multiplication.

How can you check the answer when a division problem has a remainder?

11. Leon has 1,353 bottle caps in his collection.

He decides to divide them evenly among

47 boxes. How many bottle caps will Leon

have left over?

12. It takes 48 ounces of vegetable broth to make

a pot of Chef Zoe’s minestrone soup. How

many pots of soup can be made with

432 ounces of broth?

2.6 Divide by 2-Digit Divisors

Number and Operations—5.3.CAlso 5.3.AMATHEMATICAL PROCESSES 5.1.B

43 r9

168

131

214 r14

2 r47

26

15 r51

194 r40

40 r13

Possible answer: After the quotient and divisor are multiplied, the remainder

must be added to get the dividend.

37 bottle caps 9 pots

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Module 2 • Lesson 6 89

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Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

89-90 Module 2